Finite Group Databasebeta

← #13071948

Subgroups — #13071948

Order 1408.

864 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4341C211yesmaximal, characteristic
2C2×C11×#123C211yesmaximal, characteristic, complemented
3C2×#66982C211yesmaximal, characteristic, complemented
4C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#10622833C211yesmaximal, characteristic, complemented
6#10622602C212yesmaximal, complemented
7#10622592C212yesmaximal, complemented
8#10622572C212yesmaximal, complemented
9#10622571C211yesmaximal, characteristic, complemented
10#10622559C212yesmaximal, complemented
11#10622556C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C22×C22⋊D11C2211yescharacteristic
16C23×Dic11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C23×Dic11C2211yescharacteristic
19C2×#4341—24no—
20C2×#4341—24no—
21C2×#4341—24no—
22C22×C4×D11C2211yescharacteristic
23C22×Dic22C2211yescharacteristic
24C11×#123—24no—
25C2×C11×C4⋊C4C2212yes—
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2212yes—
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2212yes—
30#66982—24no—
31C2×(C2×D11)⋊C4C2212yes—
32C2×(C2×D11)⋊C4C2212yes—
33C2×Dic11⋊C4—24no—
34C2×Dic11⋊C4C2212yes—
35C2×Dic11⋊C4C2212yes—
36C2×Dic11⋊C4C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C11⋊#95C2212yes—
40C11⋊#95C2212yes—
41C24×C11C2311yescharacteristic
42C24×C11C2311yescharacteristic
43C23×D11C2311yescharacteristic
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11D414yes—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11C2312yes—
51C22×C4×C11C2312yes—
52C22×C4×C11C2311yescharacteristic
53C2×C22⋊D11—22no—
54C2×C22⋊D11—22no—
55C2×C22⋊D11—22no—
56C2×C22⋊D11—22no—
57C2×C22⋊D11—22no—
58C2×C22⋊D11D414yes—
59C22×Dic11—22no—
60C22×Dic11—22no—
61C22×Dic11—24no—
62C22×Dic11—22no—
63C22×Dic11—22no—
64C22×Dic11—22no—
65C22×Dic11—22no—
66C22×Dic11D414yes—
67C22×Dic11C2312yes—
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2312yes—
72#4341—232no—
73C2×C4×D11—22no—
74C2×C4×D11—22no—
75C2×C4×D11—22no—
76C2×Dic22—22no—
77C2×Dic22—22no—
78C2×Dic22—22no—
79C11×C4⋊C4—24no—
80C11×C22⋊C4—22no—
81C11×C22⋊C4—24no—
82C22⋊Dic11—24no—
83C22⋊Dic11—22no—
84(C2×D11)⋊C4—24no—
85(C2×D11)⋊C4—24no—
86Dic11⋊C4—24no—
87Dic11⋊C4—24no—
88Dic11⋊C4—24no—
89#2406—111nomaximal, Sylow
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—22no—
95C23×C11—22no—
96C23×C11C2×D412yes—
97C23×C11C2×D412yes—
98C23×C11C2×D412yes—
99C23×C11C2×D412yes—
100C23×C11C2411yescharacteristic
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—22no—
104C22×D11—22no—
105C22×D11C2×D412yes—
106D4×C11—28no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—44no—
116C2×C4×C11C2×D412yes—
117C22⋊D11—28no—
118C22⋊D11—28no—
119C2×Dic11—28no—
120C2×Dic11—28no—
121C2×Dic11—28no—
122C2×Dic11—22no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11C2×D412yes—
134C2×Dic11C2×D412yes—
135C2×Dic11C2×D412yes—
136C2×Dic11#4114yescomplemented
137C4×D11—28no—
138Dic22—28no—
139C22×#41—111no—
140C2×#123—111no—
141C2×#123D1111yescharacteristic, complemented
142C22×C4⋊C4—111no—
143#395—112no—
144#394—112no—
145#386—111no—
146#386—111no—
147#385—112no—
148#385—112no—
149#381—111no—
150C22×C11—22no—
151C22×C11—22no—
152C22×C11—24no—
153C22×C11—24no—
154C22×C11—22no—
155C22×C11—24no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—42no—
159C22×C11#12014yes—
160C22×C11C22×D411yescharacteristic
161C22×C11C22×D411yescharacteristic
162C22×C11C22×D411yescharacteristic
163C22×C11C2×#4112yes—
164C22×C112−1+412yes—
165C2×D11—22no—
166C2×D11—24no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—42no—
170C4×C11—22no—
171C4×C11—42no—
172C4×C11—42no—
173Dic11—22no—
174Dic11—22no—
175Dic11—22no—
176Dic11—24no—
177Dic11—42no—
178C2×#41—224no—
179C2×#41—224no—
180C2×#41—224no—
181C22×Q8—111no—
182C22×D4—111no—
183C22×D4—111no—
184C22×D4C2×D1111yescharacteristic
185C23×C4—111no—
186C23×C4—111no—
187C23×C4—111no—
188C23×C4—111no—
189C23×C4C2×D1111yescharacteristic
190#123—24no—
191#123—224no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—112no—
194C2×C4⋊C4—112no—
195C2×C4⋊C4—224no—
196C2×C4⋊C4C2×D1112yes—
197C2×C22⋊C4—111no—
198C2×C22⋊C4—112no—
199C2×C22⋊C4—112no—
200C2×C22⋊C4—112no—
201C2×C22⋊C4C2×D1111yescharacteristic
202C2×C22⋊C4C2×D1112yes—
203#95—112no—
204#95—112no—
205#95—112no—
206#95—112no—
207C2×C11—24no—
208C2×C11—42no—
209C2×C11C2×#12011yescharacteristic
210C2×C11#52511yescharacteristic
211C2×C11#53611yescharacteristic
212C2×C11#54712yes—
213C2×C11#54712yes—
214D11—42no—
215C24—111no—
216C24C22×D1111yescharacteristic
217C24C22×D1111yescharacteristic
218#41—2232no—
219C2×Q8—222no—
220C2×Q8—222no—
221C2×Q8—222no—
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—114no—
225C2×D4—222no—
226C2×D4—222no—
227C2×D4—222no—
228C2×D4—222no—
229C2×D4—222no—
230C2×D4C22⋊D1114yes—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—114no—
235C22×C4—112no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—112no—
240C22×C4—222no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4—222no—
244C22×C4—224no—
245C22×C4—222no—
246C22×C4—222no—
247C22×C4—222no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4C22×D1112yes—
251C22×C4C22×D1112yes—
252C22×C4C22×D1111yescharacteristic
253C4⋊C4—24no—
254C4⋊C4—224no—
255C4⋊C4—224no—
256C4⋊C4—224no—
257C22⋊C4—22no—
258C22⋊C4—24no—
259C22⋊C4—224no—
260C22⋊C4—224no—
261C22⋊C4—224no—
262C22⋊C4—222no—
263C11#240611yescharacteristic, complemented, Sylow
264C23—22no—
265C23—22no—
266C23—21no—
267C23—21no—
268C23—22no—
269C23—22no—
270C23—112no—
271C23—221no—
272C23—222no—
273C23—222no—
274C23—221no—
275C23D4×D1112yes—
276C23D4×D1112yes—
277C23C2×C22⋊D1112yes—
278C23C2×C22⋊D1112yes—
279C23C23×D1111yescharacteristic
280Q8—228no—
281D4—28no—
282D4—228no—
283D4—228no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—44no—
293C2×C4—112no—
294C2×C4—112no—
295C2×C4—112no—
296C2×C4—114no—
297C2×C4—228no—
298C2×C4—228no—
299C2×C4—228no—
300C2×C4—228no—
301C2×C4—222no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—222no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4C2×C22⋊D1112yes—
313C22—24no—
314C22—22no—
315C22—24no—
316C22—22no—
317C22—22no—
318C22—24no—
319C22—41no—
320C22—42no—
321C22—41no—
322C22—222no—
323C22—224no—
324C22—442no—
325C22—441no—
326C22—441no—
327C22#6699014yes—
328C22C2×D4×D1111yescharacteristic
329C22C2×D4×D1111yescharacteristic
330C22#41×D1112yes—
331C22#6704312yes—
332C22C22×C22⋊D1111yescharacteristic
333C4—22no—
334C4—42no—
335C4—42no—
336C4—222no—
337C4—222no—
338C4—222no—
339C4—224no—
340C4—442no—
341C2—24no—
342C2—42no—
343C2—442no—
344C2#1062317911yescharacteristic
345C2#1062318612yes—
346C2#1062318711yescharacteristic
347C2C2×#6699011yescharacteristic
348C2#1062335512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#123C2
prime radicalC22×#4341C2
hypercenterC2×#123D11
hypocenterC11#2406
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C11×#123C2semidirect
3. C2×#66982C2semidirect
4. C22×Dic11⋊C4C2semidirect
5. #10622833C2semidirect
6. #10622602C2semidirect
7. #10622592C2semidirect
8. #10622572C2semidirect
9. #10622571C2semidirect
10. #10622559C2semidirect
11. #10622556C2semidirect
136. C2×Dic11#41semidirect
141. C2×#123D11semidirect
263. C11#2406semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#43412
C2×C11×#1232
C2×#669822
C22×Dic11⋊C42
#106228332
#106226022
#106225922
#106225722
#106225712
#106225592
#106225562
#240611